论文标题
平面$ \ mathcal {n} = 4 $ sym的横向动量扩展的异常维度
Anomalous dimension of transverse momentum broadening in planar $\mathcal{N}=4$ SYM
论文作者
论文摘要
典型的横向动量$ q_s（t）$（或“饱和度”动量）是由通过$ \ MATHCAL {n} = 4 $ SYMPASMA传播的硬粒子所获得的，如$ t^γ$，具有异常指数$γ> 1/2 $的特征，例如$ t^γ$。此异常指数是't Hooft耦合$λ= g^2n_c $的函数。最近，已经提出了一种方法来系统地计算弱耦合时$γ（λ）$的扰动系列。这种方法依赖于$ q_s（t）$的时间演变的行动波解释以及在很大程度上软性辐射校正的主导地位。在本文中，我们使用bfkl方程在平面$ \ mathcal {n} = 4 $ syms中的bfkl方程的双对数行为来计算$γ（λ）$最高$ \ mathcal {o}（λ^{2}）$。该计算使我们能够讨论向强耦合方案的过渡，在该耦合方案中，ADS/CFT计算预测$γ\至1 $。
The typical transverse momentum $Q_s(t)$ (or "saturation" momentum) acquired by a hard particle propagating through a $\mathcal{N}=4$ SYM plasma increases over time like $t^γ$, with an anomalous exponent $γ>1/2$ characteristic of super-diffusion. This anomalous exponent is a function of the 't Hooft coupling $λ=g^2N_c$. Recently, a method has been proposed to systematically compute the perturbative series of $γ(λ)$ at weak coupling. This method relies on the traveling wave interpretation of the time evolution of $Q_s(t)$ and on the dominance of soft-collinear radiative corrections at large times. In this paper, we compute $γ(λ)$ up to $\mathcal{O}(λ^{2})$ using the double logarithmic behaviour of the BFKL equation in planar $\mathcal{N}=4$ SYM at three loops. This calculation allows us to discuss the transition towards the strong coupling regime where AdS/CFT calculations predict $γ\to 1$.
